Mathematical Sciences: Geometric Approach to Weinstein Conjecture

主要研究者将研究紧密接触流形的接触叶中紧密叶的存在性。这些叶子的存在是由温斯坦推测出来的。这个研究者和其他数学家已经解决了几个特殊情况。licorish外科技术将用于研究问题的三维版本。Okumura的理论将应用于Kaehler流形中具有接触类型的超曲面的问题。微分同胚群也将被研究。“流形”是广义曲面。它们可能被低维度的“叶子”集合填充。这样的叶子集合被称为“叶”。首席研究员将研究那些不是连续缠绕但实际上是闭合的叶子。这些在文献中被称为“致密叶”。这在其他科学的应用中尤为重要，因为它们在一般意义上代表了无限重复的行为。

The principal investigator will study the existence of compact leaves in contact foliations of compact contact manifolds. The existence of these foliations was conjectured by Weinstein. Several special cases have been solved by this investigator and by other mathematicians. Lickorish surgical techniques will be used to investigate the three-dimensional version of the problem. Okumura's theory will be applied to the problem in the case of hypersurfaces with contact types in Kaehler manifolds. Diffeomorphism groups will also be studied. "Manifolds" are generalized surfaces. These may be filled with collections of lower dimensional "leaves." Such collections of leaves are called "foliations." The principal investigator will study leaves which do not wrap on continuously but actually close up. These are called in the literature, "compact leaves." Such are particularly important in applications to other sciences in that they represent, in a general sense, behavior which repeats indefinitely.